A Pompeo exit would be a blow to the Trump administration, which has lost several high-profile officials in the past year, including Defense Secretary James Mattis and Attorney General Jeff Sessions along with White House chief of Staff John Kelly.

President Donald Trump said he spoke to Secretary of State Mike Pompeo and 'he tells me he wouldn't want to leave' his administration to run for the Senate

Secretary of State Mike Pompeo is said to be Trump's favorite Cabinet member

Pompeo tweeted on Sunday his love for his job but did not address whether or not he'd leave his post as America's top diplomat to run for the Senate.

'It's true @realDonaldTrump, I do love being America's most senior diplomat. I love it because I get to lead the great men and women of @StateDept who bust their tails every day to proudly deliver American values and American diplomacy to every corner of the world. #Swagger,' he wrote.

When longtime Republican Sen. Pat Roberts decided to retire last month, some Republican senators - including GOP Leader Mitch McConnell - tried to recruit Pompeo to return to his home state and run in 2020.

Trump initially said it was 'fake news' McConnell tried to recruit his secretary of state.

'That was fake news,' he said.

But when CBS' Margaret Brennan pointed out Pompeo 'said McConnell had spoken to him about running for the Senate,' Trump backed down.

'Well, he may have spoken to him, but I think he loves being secretary of state. He's doing a fantastic job. And I asked him the question the other day, he says he's absolutely not leaving. I don't think he'd do that. And he doesn't want to be lame duck. And he's doing a fantastic job as our secretary of state. Great energy and great - a great, smart gentleman,' he said.

Pompeo is Trump's favorite Cabinet member, The Washington Post reported, and the president is said not to want to lose him.

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Pompeo represented Kansas in the House for four terms before becoming Trump's CIA director and then moving over to the State Department.

Last month, Pompeo confirmed to Fox News that McConnell had asked him to consider running for the Senate seat.

'Lots of folks have reached out to me and suggested I ought to do it,' Pompeo told the news network. 'I have suggested to them that I have a very full plate as secretary of state and I intend to keep doing this so long as President Trump will commit to it.'

There are concerns among Republicans Democrats could take the long time GOP seat if 2020 is a wave election for Democrats in the Senate. The GOP picked up four Senate seats held by Democrats in states that Trump won last year.

The president expressed general faith in his cabinet during his interview with CBS despite the high turnover: his original secretaries of state, defense, and interior are gone along with his attorney general.

Secretary of State Mike Pompeo tweeted Sunday his love for his job but did not address whether or not he'd leave his post as America's top diplomat to run for the Senate

Trump claimed to CBS he asked Defense Secretary James Mattis to resign when he disagreed with the job he was doing

'How do you know when to fire someone?,' CBS' Margaret Brennan asked him.

'When it's not happening,' Trump said.

The president went on to cite former Defense Secretary James Mattis, whom he fired after Mattis took some shots at him in his resignation letter.

'Like with General Mattis, I wasn't happy with his service. I told him give me a letter,' Trump said.

'He resigned,' Brennan pointed out.

'He resigned because I asked him to resign. He resigned because I was very nice to him. But I gave him big budgets and he didn't do well in Afghanistan. I was not happy with the job he was doing in Afghanistan. And if you look at Syria what's happened, I went to Iraq recently, if you look at Syria, what's happened in Syria in the last few weeks, you would see that things are going down that were not going down. That things are happening that are very good. So I was not happy with him, but I wish him well,' he said.

Mattis turned in his notice when he disagreed with the president's decision to withdraw U.S. forces from Syria.